San Diego Padres

The San Diego Padres selected Barbato in the sixth round, with the 184th overall selection, of the 2010 Major League Baseball draft, and he signed with San Diego rather than attend college.^[2] He made his professional debut in 2011 with the Low–A Eugene Emeralds, posting a 4.89 ERA with 50 strikeouts in 15 appearances (13 starts).^[3] Barbato spent the 2012 season with the Single–A Fort Wayne TinCaps, making 48 appearances out of the bullpen and logging a 6–1 record and 1.84 ERA with 84 strikeouts across 73+1⁄3 innings.^[4]

In 2013, Barbato made 49 appearances for the High–A Lake Elsinore Storm, registering a 5.01 ERA with 89 strikeouts and 14 saves across 88 innings pitched.^[5] He made 27 relief outings for the Double–A San Antonio Missions in 2014, recording a 2.87 ERA with 33 strikeouts and 16 saves across 31+1⁄3 innings of work.^[6]

New York Yankees

On December 29, 2014, the Padres traded Barbato to the New York Yankees in exchange for Shawn Kelley.^[7] He made 40 appearances split between the Double–A Trenton Thunder and Triple–A Scranton/Wilkes-Barre RailRiders, accumulating a 6–2 record and 2.67 ERA with 70 strikeouts in 67+1⁄3 innings. The Yankees added him to their 40-man roster after the 2015 season.^[8]

Barbato made his major league debut on April 5, 2016. He was optioned down to Triple–A Scranton on May 9,^[9] recalled on August 4, and sent back again on August 6. In 13 games with the Yankees in 2016, Barbato had a 1–2 record with a 7.62 ERA.

Pittsburgh Pirates

Barbato was designated for assignment by the Yankees at the start of the 2017 season and sent to Scranton/Wilkes-Barre. He was subsequently traded to the Pittsburgh Pirates on April 17, 2017, in exchange for Matt Frawley.^[10][11] In 24 relief appearances for the Pirates, Barbato posted a 4.08 ERA with 23 strikeouts in 28+2⁄3 innings.

Detroit Tigers

On January 11, 2018, Barbato was claimed off waivers by the Detroit Tigers.^[12] After starting the season with the Triple–A Toledo Mud Hens, Barbato was called up on April 26 and made his Tigers debut the following night against the Baltimore Orioles.^[13] Barbato was next called up on May 30, 2018.^[14] He was called up again on June 20, 2018.^[15] After giving up five earned runs in less than an inning two days later, Barbato was placed on the 10-day disabled list with shoulder tightness.^[16] He failed to mention previously that the injury had been bothering him all season, which left manager Rod Gardenhire somewhat perplexed since he asked to throw a light bullpen session earlier that day.^[17] He was designated for assignment on September 11, 2018.^[18] He was sent outright to the Toledo Mud Hens after clearing waivers two days later.^[19] Barbato elected free agency on November 2, 2018.^[20]

Hokkaido Nippon-Ham Fighters

On December 20, 2018, Barbato signed with the Hokkaido Nippon-Ham Fighters of Nippon Professional Baseball. He was released on October 18, 2019.^[21]

On October 11, 2019, Fighters announced that team will not sign with Barbato for next season.^[22] On October 18, 2019, he become free agent.^[23]

Somerset Patriots

On January 27, 2020, Barbato signed with the Somerset Patriots of the Atlantic League of Professional Baseball. Barbato did not appear for the club in 2020 due to the cancellation of the ALPB season because to the COVID-19 pandemic. In July 2020, Barbato signed on to play for the Sugar Land Lightning Sloths of the Constellation Energy League (a makeshift 4-team independent league created as a result of the COVID-19 pandemic) for the 2020 season.^[24] Barbato became a free agent after the year.

Lincoln Saltdogs

On January 27, 2021, Barbato signed with the Lincoln Saltdogs of the American Association of Professional Baseball.^[25] Barbato recorded a 0.90 ERA in 2 appearances for the Saltdogs, striking out 12 in 10.0 innings of work.

Toronto Blue Jays

On June 1, 2021, Barbato's contract was purchased by the Toronto Blue Jays organization.^[26]

High Point Rockers

On April 21, 2022, Barbato signed with the High Point Rockers of the Atlantic League of Professional Baseball.^[27] Barbato did not make an appearance for the Rockers before retiring from professional baseball on July 24.^[28]